3.Let G be an arbitrary group, H1,…,Hn some (not necessarily distinet) subgroup of G and g1,…,gn elements of G such that each element of G belongs at least to one of the right cosets H1g1,…,Hngn. Show that if, for any k, the set-union of the cosets Higi(i=1,…,k−1,k+1,…,n) differs from G, then every Hk(k=1,…,n) is of finite index in G. (A. 15) group theoryabstract algebracollege contests